When dealing with relatively large amounts of digital numbers which vary radically in amplitude or size it is imperative that the system incorporate appropriate adaptive scaling if the system is to maintain a high degree of numerical accuracy. In a digital system where each number is represented by a digital word having a plurality of bits and the system performs a variety of mathematical operations, small and extremely small numbers can be lost completely in the operations without some form of adaptive scaling. Adaptive scaling basically involves starting at the left (most significant bit) and searching toward the right for the first most significant magnitude bit and then shifting the entire word to the left the number of bits required to place the most significant magnitude bit in the second most significant bit location of the digital word. This is generally referred to as "left justifying" the digital word. In adaptive scaling systems it is, of course, necessary to remember the number of bits that each word is left-shifted since each shift represents multiplication by 2. Thus, when a digital word is shifted three bits to the left, a 2.sup.3 multiplication factor must be associated with the number represented by the digital word.
Adaptive scaling also includes shifting, of previously scaled digital words, up or down so that the bits of the digital word will correspond with other digital words so that addition or subtraction, may be performed properly.